Asymptotics of the Solution of the Bisingular Dirichlet Problem for a Ring with an Intermediate Boundary Layer

Uniform asymptotic expansion of solution of Dirichlet boundary value problem for an elliptic type linear inhomogeneous differential equation of the second order with a small parameter at the Laplacian is constructed. A feature of the considered boundary value problem is that the corresponding unpert...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2023-10, Vol.44 (10), p.4393-4400
Main Authors: Tursunov, D. A., Zulpukarov, A. Z., Mamytov, A. O.
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Analysis
Asymptotic methods
Asymptotic series
Boundary layers
Boundary value problems
Differential equations
Dirichlet problem
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
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Summary:Uniform asymptotic expansion of solution of Dirichlet boundary value problem for an elliptic type linear inhomogeneous differential equation of the second order with a small parameter at the Laplacian is constructed. A feature of the considered boundary value problem is that the corresponding unperturbed equation has a singularly circle at the domain. Generalized method of boundary functions is applied for construction of uniform asymptotic solution to bisingular Dirichlet problems for a linear elliptic equation in a ring with an intermediate boundary layer. The resulting decomposition of solution is asymptotic in the sense of Erdelyi. The asymptotic expansions of solutions of boundary value problems are substantiated. Our goal propose is to have a simpler algorithm for constructing an asymptotics solutions of bisingular boundary value problem with intermediate boundary layer.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080223100414